The first thing that strikes me is that if the other guy has a knife and you pull one you've just started a fight. In that situation you have two lethal weapons and unless you have the bigger knife and the balls to gut the other guy before he moves you're going to get cut bad. So that means pulling a knife if the other guy pulls one is a bad idea, no matter how it goes.

On the other hand if you pull a knife the other guy might pull a bigger knife or a gun, in which case you have to gut him again. Only this time because you waited for him to pull his weapon you've lost the initiative. So that's a bad idea.

Running might work, unless he's/they're faster, or can throw knives, or have a gun. So maybe you still get cut/shot/ Maybe you bleed out later in a ditch. Still not good.

Backing away slowly, getting to a place with people or handing over cash if that's what they want is probably your best bet. Even then things could go very bad and you could end up dead.

The only good way to carry a knife would seem to be to look scary so that people decide to mess with someone else instead. It would need to be a big knife and also visible. I believe that's what my Dad did in certain parts of the tropics. No use in London though, unless you figure prison is safer.